Many Particle Hardy-Inequalities

In this paper we prove three differenttypes of the so-called many-particle Hardy inequalities. One of them is a "classical type" which is valid in any dimesnion $d\neq 2$. The second type deals with two-dimensional magnetic Dirichlet forms where every particle is supplied with a soplenoid. Finally we show that Hardy inequalities for Fermions hold true in all dimensions.Comment: 20 page

Structuring of sapphire by laser-assisted methods, ion-beam implantation, and chemical wet etching

Sapphire is an attractive material for micro- and opto-electronic systems applications because of its excellent mechanical and chemical properties. However, because of its hardness, sapphire is difficult to machine. Titanium-doped sapphire is a well-known broadly tunable and short-pulse laser material and a promising broadband light source for applications in low-coherence interferometry. We investigated several methods to fabricate rib structures in sapphire that can induce channel waveguiding in Ti:sapphire planar waveguides. These methods include direct laser ablation, laser-micromachined polyimide stripes, selective reactive ion etching, and ion-beam implantation followed by chemical wet etching. Depending on the method, we fabricated channels with depths of up to 1.5 µm. We will discuss and compare these methods. Reactive ion etching through laser-structured polyimide contact-masks has so far provided the best results in terms of etching speed and roughness of the etched structures

Ozone Oxidizes Glutathione to a Sulfonic Acid

Biosurfaces are universally covered with fluid microfilms containing reduced glutathione (GSH) and other antioxidants whose putative roles include the detoxification of ambient ozone (O_3). It is generally believed that O_3 accepts an electron from the thiolate GS^(2-) function [pK_a(GS^-) = 8.8] of GSH to produce thiyl GS^(•-) radicals en route to the disulfide GSSG. Here, we report novel electrospray mass spectrometry experiments showing that sulfonates (GSO_3^-/GSO_3^(2-)), not GSSG, are the exclusive final products on the surface of aqueous GSH microdroplets exposed to dilute O_3(g) for ~1 ms. The higher reactivity of the thiolate GS^(2-) toward O_3(g) over the thiol GS^- is kinetically resolved in this time frame due to slow GS^- acid dissociation. However, our experiments also show that O_3 will be largely scavenged by the more reactive ascorbate coantioxidant in typical interfacial biofilms. The presence of GSSG and the absence of GSO_3^-/GSO_3^(2-) in extracellular lining fluids are therefore evidence of GSH oxidation by species other than O_3

Wave-number dependence of the transitions between traveling and standing vortex waves and their mixed states in the Taylor-Couette system

Previous numerical investigations of the stability and bifurcation properties of different nonlinear combination structures of spiral vortices in a counterrotating Taylor-Couette system that were done for fixed axial wavelengths are supplemented by exploring the dependence of the vortex phenomena waves on their wavelength. This yields information about the experimental and numerical accessability of the various bifurcation scenarios. Also backwards bifurcating standing waves with oscillating amplitudes of the constituent traveling waves are found.Comment: 4 pages, 5 figure

Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators

Many engineering structures are composed of weakly coupled sectors assembled in a cyclic and ideally symmetric configuration, which can be simplified as forced Duffing oscillators. In this paper, we study the emergence of localized states in the weakly nonlinear regime. We show that multiple spatially localized solutions may exist, and the resulting bifurcation diagram strongly resembles the snaking pattern observed in a variety of fields in physics, such as optics and fluid dynamics. Moreover, in the transition from the linear to the nonlinear behaviour isolated branches of solutions are identified. Localization is caused by the hardening effect introduced by the nonlinear stiffness, and occurs at large excitation levels. Contrary to the case of mistuning, the presented localization mechanism is triggered by the nonlinearities and arises in perfectly homogeneous systems